Results 1 to 7 of 7
Like Tree3Thanks
  • 1 Post By romsek
  • 1 Post By Plato
  • 1 Post By hollywood

Math Help - Evaluate the Integral

  1. #1
    sic
    sic is offline
    Newbie
    Joined
    Sep 2013
    From
    new york
    Posts
    11

    Evaluate the Integral

    Evaluate the Integral from -pi/2 to pi of 20 * abs cos(x) dx ? I got the answer -20 but it seems to be incorrect. Can anyone provide an explanation?
    Last edited by sic; February 23rd 2014 at 03:22 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    2,773
    Thanks
    1140

    Re: Evaluate the Integral

    Quote Originally Posted by sic View Post
    Evaluate the Integral from -pi/2 to pi of 20 * abs cos(x) dx ? I got the answer -20 but it seems to be incorrect. Can anyone provide an explanation?
    well let's take a look

    $$\int_{-\frac{\pi}{2}}^{\pi}20\left|\cos(x)\right|dx = $$

    $$20\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\cos(x)dx -20\int_{\frac{\pi}{2}}^{\pi}\cos(x)dx$$

    see if you can complete it
    Thanks from sic
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,916
    Thanks
    1762
    Awards
    1

    Re: Evaluate the Integral

    Quote Originally Posted by sic View Post
    Evaluate the Integral from -pi/2 to pi of 20 * abs cos(x) dx ? I got the answer -20 but it seems to be incorrect. Can anyone provide an explanation?
    $\displaystyle\int_{ - {2^{ - 1}}\pi }^\pi {20\left| {\cos (x)} \right|dx} = \int_{ - {2^{ - 1}}\pi }^{{2^{ - 2}}\pi } {20\cos (x)dx} - \int_{{2^{ - 1}}\pi }^\pi {20 {\cos (x)} dx} $

    RECALL that $\cos(x)$ is an even function. So what is that first integral?
    Last edited by Plato; February 23rd 2014 at 03:40 PM.
    Thanks from sic
    Follow Math Help Forum on Facebook and Google+

  4. #4
    sic
    sic is offline
    Newbie
    Joined
    Sep 2013
    From
    new york
    Posts
    11

    Re: Evaluate the Integral

    cos(pi/2) and cos(-pi/2) = 0 so the first integral would be 0? Then for the second integral cos(pi) = -1 and cos (pi/2) = 0 so it would be -20? 0 - (-20) = 20?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,916
    Thanks
    1762
    Awards
    1

    Re: Evaluate the Integral

    Quote Originally Posted by sic View Post
    cos(pi/2) and cos(-pi/2) = 0 so the first integral would be 0? Then for the second integral cos(pi) = -1 and cos (pi/2) = 0 so it would be -20? 0 - (-20) = 20?
    It has nothing to do with that because $\int {\cos (x)dx = \sin (x) + c} $
    Follow Math Help Forum on Facebook and Google+

  6. #6
    sic
    sic is offline
    Newbie
    Joined
    Sep 2013
    From
    new york
    Posts
    11

    Re: Evaluate the Integral

    I found out what I did wrong, the derivative of cos(x) = sin(x) and then sin (pi/2) = 1 and sin (-pi/2) = -1 so sin(pi/2) - sin (-pi/2) = 2 and 20*2 = 40 while the next term sin (pi) =0 and sin (pi/2) = 1 so 0-1 = -1 and 20*-1 = -20. After that, by subtracting the two terms, 40- (-20) = 60.

    But how do you know where to split the integral?Are there any definitions as to how to split an abs( ) integral?
    Last edited by sic; February 23rd 2014 at 07:14 PM.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member
    Joined
    Mar 2010
    Posts
    993
    Thanks
    244

    Re: Evaluate the Integral

    Plato and romsek split the integral at pi/2 since cos(x) crosses the x-axis there. So abs(cos(x)) = cos(x) before that and abs(cos(x)) = -cos(x) after that. That's typical for integrals of functions containing absolute values.

    - Hollywood
    Thanks from sic
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: November 27th 2012, 01:51 PM
  2. Replies: 2
    Last Post: August 31st 2010, 08:38 AM
  3. Replies: 1
    Last Post: June 2nd 2010, 03:25 AM
  4. Replies: 1
    Last Post: November 28th 2009, 09:44 AM
  5. Evaluate integral
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 21st 2008, 03:42 AM

Search Tags


/mathhelpforum @mathhelpforum